Marco Benini, Jonathan P. Pridham, Alexander Schenkel
January 25, 2022
We study the quantization of the canonical unshifted Poisson structure on the derived cotangent stack $T^\ast[X/G]$ of a quotient stack, where $X$ is a smooth affine scheme with an action of a (reductive) smooth affine group scheme $G$. This is achieved through an \'etale resolution of $T^\ast[X/G]$ by stacky CDGAs that allows for an explicit description of the canonical Poisson structure on $T^\ast[X/G]$ and of the dg-category of modules quantizing it. These techniques are applied to construct a dg-category-valued prefactorization algebra that quantizes a gauge theory on directed graphs.
Keywords:Derived algebraic geometry, derived cotangent stack, quotient stack, Deformation quantization, lattice gauge theory